Write the equation of a line that is perpendicular to $y=5$ and that passes through the point $(-7,-5)$.
Explanation: Getting started Key idea: The slopes of perpendicular lines are negative reciprocals of each other. Step 1: Find the slope Where is the slope? There is no $x$ -term in the equation, so $x$ has a coefficient of $0$. The slope of the given line: ${0}={\dfrac{0}{1}}$ So, the slope of the perpendicular line: $C{\dfrac{1}{0}} C{\text{\ \ is \ undefined}}$ Note, because the given line is horizontal, we expect the perpendicular line to be vertical. Step 2: Find the x-intercept Lines with undefined slopes have the form of $x=c$, where $c$ is the $x$ -intercept. The perpendicular line will pass through the point ${(-7,-5)}$, so the $x$ -intercept is $-7$. Answer $x=-7$. ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ $y$ $x$